ABOUT:
■ As a particle, が usually indicates the sentence subject. Let's look at が as a conjunction that combines two sentences to express contrastive thoughts. In other words, "but."
While this is the most common usage, it can be used simply as a transition word to combine two sentences without necessarily contrasting.
HOW to use:
■ Sentence 1 + が + Sentence 2
[Both sentences need to be in the same formal or informal form.]
CONTRASTIVE EXAMPLE:
スーパーに行ったが、パンがなかった。
I went to the supermarket, but there was no bread.
Let's break that into two sentences:
スーパーに行った。 (I) went to the supermarket.
が but
パンがなかった。 There was no bread.
NON-CONTRASTIVE EXAMPLE:
映画を見に行きますが、来ませんか?
I'm going to see a movie. Won't you come?
In this case, you are using が as a softener. It is used to show you are casually bringing up the subject just in case the offer is rejected and you lose face.